solve for x,y

@arka .. that is definitely NOT the case.. u can break 4 into infinitely many ways...

add both equations. we get
(x+y)² + (x+y) = 30
taking x+y = t, we get

t² +t -30 = 0
=> t = 5, -6

=> x+y = 5, -6

CASE I, x+y = 5
subtract both equations,
(x+y)(x-y) - (x-y) = 4
=> 4(x-y) = 4
=> x-y = 1 and x+y = 5
solving we get x = 3, y = 2

CASE II, x+y = -6
subtracting both equations,
(x+y)(x-y) - (x-y) = 4
=> -7(x-y) = 4
=> x-y = -4/7 and x+y = -6

=> x = -23/7 and y = -19/7

just hope there arent any calculation errors